On the stability of homogeneous vector bundles

Biswas, Indranil (2004) On the stability of homogeneous vector bundles Journal of Mathematical Sciences (University of Tokyo), 11 (2). pp. 133-140. ISSN 1340-5705

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Official URL: http://journal.ms.u-tokyo.ac.jp/abstract/jms110202...


Let G be a connected semisimple linear algebraic group over an algebraically closed field k and P ⊂ G a parabolic sub-group without any simple factor. Let V be an irreducible P-module and EP (V ) = (G× V)/P the associated vector bundle over G/P. We prove that EP (V ) is stable with respect to any polarization on G/P. In [Um] this was proved under the assumption that the characteristic of k is zero and the question was asked whether it remains valid when the characteristic is positive.

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